The document is solving a math problem to find the length of a chord that subtends an angle of 90 degrees in a circle with a radius of 8cm. It shows that the length of the chord can be found using either the cosine rule or Pythagorean theorem since the triangle formed is a right triangle. Applying either formula, the length of the chord is calculated to be 8√2 cm, which is option B. The key steps are drawing a diagram of the circle and right triangle, then applying either the cosine rule or Pythagorean theorem to solve for the missing side.
Areas related to circles - Area of sector and segment of a circle (Class 10 m...Let's Tute
Areas related to circles - Area of sector and segment of a circle (Class 10 maths).
Let's tute is an E-school or E- platform which is free for the student.Students will watch "MATHS" Videos for conceptual understanding.
Contact Us -
Website -www.letstute.com
YouTube - www.youtube.com/letstute
Areas related to circles - Area of sector and segment of a circle (Class 10 m...Let's Tute
Areas related to circles - Area of sector and segment of a circle (Class 10 maths).
Let's tute is an E-school or E- platform which is free for the student.Students will watch "MATHS" Videos for conceptual understanding.
Contact Us -
Website -www.letstute.com
YouTube - www.youtube.com/letstute
Areas related to circles - Areas of combinations of plane figures (Class 10 M...Let's Tute
Areas related to circles - Areas of combinations of plane figures (Class 10 Maths).
Let's tute is an E-school or E- platform which is free for the student.Students will watch "MATHS" Videos for conceptual understanding.
Contact Us -
Website - www.letstute.com
YouTube - www.youtube.com/letstute
5.13.3 Geometric Probability and Changing Dimensionssmiller5
Students will
* Calculate geometric probabilities
* Use geometric probability to predict results in real-world situations
* Predict the effects of changing dimensions on the perimeter/circumference and area of a figure.
Areas related to circles - Areas of combinations of plane figures (Class 10 M...Let's Tute
Areas related to circles - Areas of combinations of plane figures (Class 10 Maths).
Let's tute is an E-school or E- platform which is free for the student.Students will watch "MATHS" Videos for conceptual understanding.
Contact Us -
Website - www.letstute.com
YouTube - www.youtube.com/letstute
5.13.3 Geometric Probability and Changing Dimensionssmiller5
Students will
* Calculate geometric probabilities
* Use geometric probability to predict results in real-world situations
* Predict the effects of changing dimensions on the perimeter/circumference and area of a figure.
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1. JAMB: Mathematics,
Question 28, 2013
Find the length of a chord which subtends an angle of 90 o at
the centre of a circle whose radius is 8cm (a) 8cm (b) 8 𝟐𝒄𝒎
(c) (d) 4cm
2. SOLUTION
Topic/Subtopic: Circles/Chord Properties
To solve this problem, let us show it on a diagram
Where 𝐴𝐵 = Length of the chord and the radius (r) = 8cm, cut out the ΔAOB
8cm8cm
0
A B
90o
Circle
Radius
Chord
3. Length 𝐴𝐵 can be obtained by cosine – Rule since two sides of a triangle and
an included angle are given (condition for applying cosine rule).
A B
0
90
8cm 8cm
4. Applying cosine – rule to the triangle we have:
• /AB/2 = /AO/2 + /BO/2 – 2/AO//BO/Cos 𝑂
• /AB/2 = 82 + 82 – (2 x 8 x 8 x cos 90o)
• /AB/2 = 64 + 64 – (128 x cos 90o)
• /AB/2 = 128 – (128 x 0) since cos 90o = 0
• /AB/2 = 128 – 0 = 128
• /AB/ = 128 = 2 𝑥 64 = 2 x 64 = 2 x 8
• Therefore, /AB/ = 8 𝟐𝒄𝒎 (Option B)
5. It is important to note that the triangle AOB is a right-angle triangle since angle
𝑂 = 90o as a result. We can also apply Pythagoras theorem to solve for /AB/ as
shown in the next slide (method 2):
6. METHOD II
We can as well draw the triangle like this:
A B
0
8cm 8cm
7. Applying Pythagoras theorem to the triangle we have:
/AB/2 = /AO/2 + /BO/2 (the square of the longest side equals the sum of the
square of the two other sides)
• /AB/2 = 82 + 82
• /AB/2 = 64 + 64
• /AB/2 = 128
• /AB/2 = 128
• /AB/2 = 2 x 64
• /AB/2 = 2 x 64
• /AB/2 = 2 x 8
• /AB/2 = 8 2𝑐𝑚
8. Final notes
(1) Pythagoras theorem is applied only when the triangle is a right-angled
triangle
(2) When two sides of a triangle are given and you are asked to find the third
side
